stay on after (something)

1. To remain in or at some place after something finishes. I was going to just go home until I found out that a number of attendees were staying on after the seminar. The teacher stays on after class on Tuesdays and Thursdays for any students who need a little extra help.

2. To remain employed at or involved in an organization after some temporary period of employment comes to an end. I had already started looking for other work, but then they gave me the option of staying on after the maternity cover was over. Is Jessica only working for the summer, or will she stay on after her internship ends?